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A pipe can fill a tank in 10 hours, while another pipe can empty it in 15 hours.

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Question: A pipe can fill a tank in 10 hours, while another pipe can empty it in 15 hours. If both pipes are opened together, how long will it take to fill the tank?

Options:

  1. 5 hours
  2. 6 hours
  3. 7 hours
  4. 8 hours

Correct Answer: 6 hours

Solution: 

The net rate of filling the tank is 1/10 - 1/15 = 1/30. Therefore, it will take 30 hours to fill the tank.

A pipe can fill a tank in 10 hours, while another pipe can empty it in 15 hours.

Practice Questions

Q1
A pipe can fill a tank in 10 hours, while another pipe can empty it in 15 hours. If both pipes are opened together, how long will it take to fill the tank?
  1. 5 hours
  2. 6 hours
  3. 7 hours
  4. 8 hours

Questions & Step-by-Step Solutions

A pipe can fill a tank in 10 hours, while another pipe can empty it in 15 hours. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 30 hours
  • Step 1: Determine the rate at which the first pipe fills the tank. It fills the tank in 10 hours, so its rate is 1 tank per 10 hours, or 1/10 of the tank per hour.
  • Step 2: Determine the rate at which the second pipe empties the tank. It empties the tank in 15 hours, so its rate is 1 tank per 15 hours, or 1/15 of the tank per hour.
  • Step 3: Calculate the net rate of filling the tank when both pipes are opened together. This is done by subtracting the emptying rate from the filling rate: (1/10) - (1/15).
  • Step 4: To subtract the fractions, find a common denominator. The least common multiple of 10 and 15 is 30.
  • Step 5: Convert the rates to have the common denominator: (1/10) = 3/30 and (1/15) = 2/30.
  • Step 6: Now subtract the two rates: (3/30) - (2/30) = 1/30.
  • Step 7: The net rate of filling the tank is 1/30 of the tank per hour. This means it takes 30 hours to fill the tank when both pipes are open.
  • Rate of Work – Understanding how to calculate the rates of filling and emptying a tank and combining them.
  • Fractional Work – Using fractions to represent the portion of the tank filled or emptied per hour.
  • Net Rate Calculation – Calculating the net effect of two opposing rates (filling and emptying) to find the overall rate.
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